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MCMCDiagnosticTools

MCMCDiagnosticTools provides functionality for diagnosing samples generated using Markov Chain Monte Carlo.

Background

Some methods were originally part of Mamba.jl and then MCMCChains.jl. This package is a joint collaboration between the Turing and ArviZ projects.

Effective sample size and $\widehat{R}$

MCMCDiagnosticTools.ess — Function
ess(
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GitHub
MCMCDiagnosticTools
MCMCDiagnosticTools provides functionality for diagnosing samples generated using Markov Chain Monte Carlo.
Background
Some methods were originally part of Mamba.jl and then MCMCChains.jl. This package is a joint collaboration between the Turing and ArviZ projects.
Effective sample size and $\widehat{R}$
MCMCDiagnosticTools.ess — Function
ess(
     samples::AbstractArray{<:Union{Missing,Real}};
     kind=:bulk,
     relative::Bool=false,
@@ -56,3 +514,4 @@
 )
Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
kwargs are forwarded to mcse.
source
MCMCDiagnosticTools.rafterydiag — Function
rafterydiag(
     x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
 )
Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy.  The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
source
  • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
  • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
  • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
  • Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
  • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
  • BDA3Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
  • FlegalJones2011Flegal JM, Jones GL. (2011) Implementing MCMC: estimating with confidence.                 Handbook of Markov Chain Monte Carlo. pp. 175-97.                 pdf
  • Flegal2012Flegal JM. (2012) Applicability of subsampling bootstrap methods in Markov chain Monte Carlo.            Monte Carlo and Quasi-Monte Carlo Methods 2010. pp. 363-72.            doi: 10.1007/978-3-642-27440-4_18
  • Betancourt2018Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]
  • Betancourt2016Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]
  • Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
  • Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
  • Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
  • Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
  • Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.

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